Former Speaker Kevin McCarthy floated the possibility on Monday that he might be open to reclaiming the post from which he was ousted less than a week ago, even as two other Republicans vied to replace him in a contest that has highlighted the party’s deep divisions.

With the House rudderless and paralyzed following Mr. McCarthy’s removal last week, the California Republican worked to project normalcy and leadership in the face of the war unfolding in Israel, after an invasion by the Palestinian militant group Hamas that has led to hundreds of deaths and the capture of scores of civilian Israeli hostages.

The appearance had all the trappings of the job he just lost; Mr. McCarthy spoke from behind a podium in the Rayburn Room, where the speaker often holds official ceremonies, and used the language of a party leader during a crisis.

2 House Republican, and Representative Jim Jordan of Ohio, the Judiciary Committee chairman — have been vying to shore up support, but the party is fractured.

With the chamber under the control of a temporary speaker, lawmakers are questioning what power, if any, they have to take action as a legislative body, including approving additional aid for Israel.

In a reflection of the uncertainty roiling their conference, Republicans scheduled a closed-door listening session on Monday, returning to Washington on a federal holiday to meet in the House basement and hash out their disagreements.

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